Again you are using a different definition of eligible. You are hung up on the way that we use that word in everyday speech. For officiating a basketball game that word takes on a very specific meaning. Basketball jargon.
The rules book usage of eligible has nothing to do with grades, transfers, residency, school attendance, discipline, etc.
Those are items that the state organization and the schools themselves determine. During the game it is the official's job to simply look who is dressed out and on the bench. Plain and simple.
I'm not trying to be difficult here, just attempting to give you some guidance. If you choose to do it differently, best wishes to ya.